CAX is a very special case! Maybe if Peel set up an airline, ...
If it was possible to operate flights to LHR I'm sure someone would be doing it, but I think it would have to be Heathrow as the train is now sufficiently competitive that operating to a London airport without lots of connecting traffic clearly wouldn't cut it.
Could BFS and DUB work? I suspect that in market organised differently they could. I feel like there's a little bit of market failure in regional air services in the UK (eg where a link like LDY - LON with clear demand can become a PSO). It's a real shame about Loganair burying the hatchet with Eastern - I really thought they might be the ones to try them!
However on the one hand the only way our regional air services could work better would be if there was an airline with many bases around the UK that was flying a range of sizes of aircraft and able to market efficiently (without worrying about marketing so well that someone would come along with a bigger aircraft and took the route off them).
But on the other hand DTV would only be served in a competitive market, because any airline that operates from a destination to NCL, LBA and DSA (and EMA) is going to see if they can get off with carrying the same number of passengers as they would if they also served MME (and HUY).
And that brings me round to the depressing conclusion; who would operate BFS or DUB? FlyBe and AerLingus (and / or Stobart) could, have bases in the right places, have the right sizes of aircraft, and serve the right types of market. But why would the bother? They're probably already carrying all the people that would book a flight to Belfast or Dublin with them :-( BMI or Eastern could in theory, but it wouldn't be a good fit with their existing networks or markets.
I would say the future carries on looking grim. Unless Stobart buy it for a distribution depot...